Geodesic
Splitting algorithms for the wavelet transform of first-degree splines on nonuniform grids
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1236-1247 
B. M. Shumilov. Splitting algorithms for the wavelet transform of first-degree splines on nonuniform grids. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1236-1247. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a2/
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     title = {Splitting algorithms for the wavelet transform of first-degree splines on nonuniform grids},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the splines of first degree with nonuniform knots, a new type of wavelets with a biased support is proposed. Using splitting with respect to the even and odd knots, a new wavelet decomposition algorithm in the form of the solution of a three-diagonal system of linear algebraic equations with respect to the wavelet coefficients is proposed. The application of the proposed implicit scheme to the point prediction of time series is investigated for the first time. Results of numerical experiments on the prediction accuracy and the compression of spline wavelet decompositions are presented.

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